Internal fluid pressure often plays an important role in the rupture of brittle materials. This is a major concern for many engineering applications and for natural hazards. More specifically, the mechanisms through which fluid pressure, applied at a microscale, can enhance the failure at a macroscale and accelerate damage dynamics leading to failure remains unclear. Here we revisit the fiber bundle model by accounting for the effect of fluid under pressure that contributes to the global load supported by the fiber bundle. Fluid pressure is applied on the broken fibers, following Biot's theory. The statistical properties of damage avalanches and their evolution toward macrofailure are analyzed for a wide range of fluid pressures. The macroscopic strength of the new model appears to be strongly controlled by the action of the fluid, particularly when the fluid pressure becomes comparable with the fiber strength. The behavior remains consistent with continuous transition, i.e., second order, including for large pressure. The main change concerns the damage acceleration toward the failure that is well modeled by the concept of sweeping of an instability. When pressure is increased, the exponent beta characterizing the power-law distribution avalanche sizes significantly decreases and the exponent gamma characterizing the cutoff divergence when failure is approached significantly increases. This proves that fluid pressure plays a key role in failure process acting as destabilization factor. This indicates that macrofailure occurs more readily under fluid pressure, with a behavior that becomes progressively unstable as fluid pressure increases. This may have considerable consequences on our ability to forecast failure when fluid pressure is acting.